YES(?,O(n^1)) 15.12/8.26 YES(?,O(n^1)) 15.12/8.26 15.12/8.26 We are left with following problem, upon which TcT provides the 15.12/8.26 certificate YES(?,O(n^1)). 15.12/8.26 15.12/8.26 Strict Trs: 15.12/8.26 { f(X) -> n__f(X) 15.12/8.26 , f(n__f(n__a())) -> f(n__g(f(n__a()))) 15.12/8.26 , a() -> n__a() 15.12/8.26 , g(X) -> n__g(X) 15.12/8.26 , activate(X) -> X 15.12/8.26 , activate(n__f(X)) -> f(X) 15.12/8.26 , activate(n__a()) -> a() 15.12/8.26 , activate(n__g(X)) -> g(X) } 15.12/8.26 Obligation: 15.12/8.26 derivational complexity 15.12/8.26 Answer: 15.12/8.26 YES(?,O(n^1)) 15.12/8.26 15.12/8.26 The problem is match-bounded by 3. The enriched problem is 15.12/8.26 compatible with the following automaton. 15.12/8.26 { f_0(1) -> 1 15.12/8.26 , f_1(1) -> 1 15.12/8.26 , f_1(2) -> 1 15.12/8.26 , f_1(4) -> 3 15.12/8.26 , f_1(5) -> 1 15.12/8.26 , f_2(5) -> 1 15.12/8.26 , f_2(7) -> 6 15.12/8.26 , n__f_0(1) -> 1 15.12/8.26 , n__f_1(1) -> 1 15.12/8.26 , n__f_2(1) -> 1 15.12/8.26 , n__f_2(2) -> 1 15.12/8.26 , n__f_2(4) -> 3 15.12/8.26 , n__f_2(5) -> 1 15.12/8.26 , n__f_3(5) -> 1 15.12/8.26 , n__f_3(7) -> 6 15.12/8.26 , n__a_0() -> 1 15.12/8.26 , n__a_1() -> 1 15.12/8.26 , n__a_1() -> 4 15.12/8.26 , n__a_2() -> 1 15.12/8.26 , n__a_2() -> 7 15.12/8.26 , n__g_0(1) -> 1 15.12/8.26 , n__g_1(1) -> 1 15.12/8.26 , n__g_1(3) -> 2 15.12/8.26 , n__g_2(1) -> 1 15.12/8.26 , n__g_2(6) -> 5 15.12/8.26 , a_0() -> 1 15.12/8.26 , a_1() -> 1 15.12/8.26 , g_0(1) -> 1 15.12/8.26 , g_1(1) -> 1 15.12/8.26 , activate_0(1) -> 1 } 15.12/8.26 15.12/8.26 Hurray, we answered YES(?,O(n^1)) 15.12/8.27 EOF